Delays constitute a key challenge in the management of service operations, causing substantial quality and cost issues. Delays in one service event can cause delays in another service event and so on, which creates challenges in the management of complex services. Assuming a lower-triangular matrix formalism, we develop a novel approach to modelling such chains of delays in complex service operations such as health care and software development. This approach can enable service managers to identify, understand, predict and control delays. Our research provides a novel theoretical contribution to the literature on service delays.